GRE
Practice Test 15
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\(\sqrt[13]{K^{7}}= 23/37\)
k \(\frac{23}{37}\)
  • Solution

    \(\sqrt[13]{K^{7}}=\frac{23}{37}\)

    ∴ \(K^{\frac{7}{13}}=\frac{23}{37}\) ∴ k = \(\left ( \frac{23}{37} \right )^{\frac{13}{7}}\)

    Since \frac{23}{37} < 1, higher powers i.e. power> 1 will have lesser values.

    ∴ \(\frac{23}{37}> \left ( \frac{23}{37} \right )^{\frac{13}{7}}\)

Each small circle above has radius x and large circle has radius y. The areas of shaded region and white region are equal.

y⁄x 2
  • Solution

    Area of shaded region =

    (πy2 - π3x2) = π(y2 - 3x2)

    Area of white region = π3x2

    ∴ π(y2 - 3x2) = π3x2

    ∴ y2 = 6x2 ∴ y⁄x = √6 > 2

θ is the sum of integers from 1 to 50, φ is the sum of integers from 51 to 100.
φ – θ 2500
  • Solution

    \(\theta =\frac{50\times 51}{2}=1275\)

    φ = \(\left ( \frac{100\times 101}{2} \right )-\frac{50\times 51}{2}=3775\)

    ∴ φ - θ = 2500

 
  • Solution

    Col. A

    XYZ is an isosceles right angle triangle.

    ∴ xy = yz = √2

    ∴ Area = 1⁄2 × √2 × √2 = 1

    Col. B

    PQR is 30° - 60° - 90° Triangle

    ∴ PQ = 1 QR = √3

    Area = 1⁄2 × 1 × √3 = .866

1⁄x = 1 + 1⁄y
x y
  • Solution

    1⁄x - 1⁄y = 1 ∴ \(\frac{y-x}{xy}=1\)

    ∴ y - x = xy

    If x and y both are positive,

    ⇒ xy is positive ⇒ y - x = positive

    ⇒ y > x

    However, if either of them is negative,

    ⇒ xy is negative ⇒ y < x is negative. ⇒ y < x

 

27 – 26 – 25 -32
  • Solution

    27 - 25 - 25 = 25(22 - 21 - 1)

    = 25 = 32

 

Angle between hour hand and minute hand of a clock at 4:20 p.m. 0°
  • Solution

    At 4:20 p.m., hour hand will move down towards 5 p.m. Therefore there will be some angle between hour hand and minute hand.

    Formula:

    (Theoretical distance in two hands × 60 ) + (Time × 1⁄2°)

    = (0 × 6°) + (20 × 1⁄2°) = 10°

    Theoretical distance is calculated assuming that hour hand does not move between 4 to 5.

A wooden cube whose edges are 4 inches is painted blue. The cube is then cut into 64 small cubes whose edges are 1 inch.
Number of small cubes that have exactly three blue faces Number of small cubes that have no blue faces.
  • Solution

    All the corners will have 3 faces painted blue.

    ∴ Col. A = 8

    Col. B The

    core of the big cube is formed of 8 small 11 inch cubes which have no face painted

    ∴ Col. B = 8

 

The arithmetic mean of all multiples of 5 less than 50 The product of first three prime numbers
  • Solution

    Col. A-

    \(\frac{5 + 10 +15 +20 + 25+ 30+ 35+40+45}{9}=25\)

    Col. B-

    2 × 3 × 5 = 30

p + x q + y
  • Solution

    P has a positive value and q is zero, (p, q) lies on x axis.

    y has a negative value and x is zero, (x, y) lies on y axis.

    ∴ p + x = p = positive number

    q + y = y = negative number

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